用泰勒公式证明极限题目!

e^x＝1＋x＋x^2/2＋o(x^2)
sinx＝x＋o(x^2)
所有,e^x－sinx－1＝1/2×x^2＋o(x^2)
√(1-x^2)＝1－1/2×x^2＋o(x^2),所以1－√(1-x^2)＝1/2×x^2＋o(x^2)
lim(x→0) [e^x－sinx－1]/[1－√(1-x^2)]
＝lim(x→0) [1/2×x^2＋o(x^2)]/[1/2×x^2＋o(x^2)]
＝lim(x→0) [1/2＋o(x^2)/x^2]/[1/2＋o(x^2)/x^2]
＝[1/2＋0]/[1/2＋0]＝1